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The Thinking Classroom experiment may be a success. The white board contact paper is starting to gather dust in the corners, the kids trust the fancy randomizer, and there are consistently good days. I’m all ready to write a post about successes or a sort of “growth” post about my what I’ve learned the most (spoiler alert: it’s about managing flow). It’s just, well…there are these two kids who I’m worried about.

On Wednesday we started on an open middle problem and two of the four pairing had a student sitting down, facing away from the board, and looking at their phone. Paul likes to mind his own business, and isn’t too interested in talking with me or any student. Denisha has flirted with pursuing a GED, with support from her parents, but decided to give this year one last shot, but so far hasn’t earned any credits in any class that didn’t her performing music. They both didn’t hear the full explanation about the class during registration, so maybe this isn’t what they expected. I am aware with both having behavior issues in previous math classes which have escalated to administrative interventions. While both of their attendance is around 50%, it surprised me that neither have had an even moderately successful day working with their groups.

On Wednesday, Paul was struggling in a grouping that made me question throwing out the randomizer. He was paired with a student who has had excellent attendance, and is pretty bright, but isn’t really a big “includer.” This student has a tendency to stare off into space, deep in thought, before emerging with an answer that he can’t seem to communicate without writing it on the board. Paul had been paired with this student before and didn’t seem to be contributing anything, even though I asked. It seemed then that Paul wasn’t being vocal then, but his body language showed he wasn’t even participating. I had to try even harder to get the marker into Paul’s hand, but he was said he “don’t learn like this.” He seemed sad that he wasn’t able to pull the answers out of the air like his groupmate and wanted me to sit next to him and tell him what to do.

The randomizer also placed Denisha in a pairing that wasn’t ideal. Her partner was probably the third least talkative kid in the class so I knew I would spend a lot of time over there getting the conversation going. The two were both quiet, Denisha seemed detached. Denisha’s partner seemed quiet because they weren’t clear about the next step in the problem, while Denisha seemed like she was trying to hide and not be seen. If I visited, she would look up and confidently assert that she knew what they were doing, but wouldn’t be able to answer any questions about the actual problem. After some questioning it seemed like she wasn’t aware of what the problem was or what her partner was doing to figure it out. When I wasn’t nearby she would zone off or get sucked back in to her phone as if she was waiting for us to go over the assignment.

Both of these students seem to struggle asserting themselves in math and are also uncomfortable with collaborating around a task. The tasks that I am giving out seem like they are pretty “low-floor,” but Paul and Denisha are not accessing or engaging with them in up until Wednesday. They don’t seem to feel safe in this environment. One of my big goals in this experiment is to create a culture where students spend more of their time feeling safe, but it seems like these two students are spending most of their time avoiding feeling “dumb.” It’s tempting to want to blame the victim here. To imagine the kids could have been more successful if they attended regularly, or to assume that these kids would “get it” if they “just got on board.” I think I should do more to meet their needs (and am open for ideas here). I’ve tried using more manipulatives and am going to work more on having students interact socially before they start working on math, but it’s hard to see if it is working or not.

On Friday I had a pretty successful day with Paul. First I explained my new grading system for the class in very clear terms. I then re-explained the whole philosophy of the class again to connect their grade to the class. Then we had the weekly quiz, which Paul would was unprepared for. Paul, and another student instead worked on quizzes from earlier weeks that they missed. Then I had those students work on a problem maximizing the area of a rectangle given a perimeter together using manipulatives. Paul was much more confident in working with this new partner, and was more vocal when I asked them to explain why they thought a square isn’t a rectangle. We ended with a conversation of what he needs to do to earn credit. I think it was a big step forward for Paul. Denisha wasn’t there, but maybe I have an approach that I can try with her. Not changing the expectations, but being as clear as possible about them, providing more ways to access the problem, and keeping to work to build confidence.

Yesterday I posted about how I began my Thinking Classroom experiment. The experiment actually started in the 2nd week of november, so at this point I’m actually 3 weeks in to it. Today I actually had the best class that I’ve had so far. It wasn’t a perfect class, but it was good enough to make me forget some of those rough days that happened along the way. There is a lot to write about, and I may not get around to it, but I will start with a digression to talk about my randomizer.

The Randomizer

Before my first class I made a randomizer that basically assigned seats to random numbers, and assigned those randomized seats to students. It was basically one that Joel Bezaire described. My school has really unpredictable attendance, however, and also has kids show up late. I needed a randomizer that wouldn’t assume that we would have the whole roster there and be smart enough to take any number of kids each day. Based on the kids in class the sheet should figure out how many pairs are needed, and then assign the random seats. This thing does all that automatically whenever a new kid is inputted into this google form that I have kids fill out (and I can also decide how many kids I want to have in each group).

It works like this. Kids fill out a google form with their names and click sign-in. This also helps me keep track of attendance and lateness. Then as the names come in, the spreadsheet puts today’s group on the right. It also automatically adds more groups as needed, and some blank seats in group “N” in case we need to form a new group. Check it out in the video below.

Bonus: If you use google slides, you can paste the two columns from the spreadsheet into your google slides, then select that you want to “link to the spreadsheet” so it will automatically fetch the new results. This way you can automatically pull up the random seatings by clicking “Update” in the slides and avoid having to even open up the spreadsheet.

This is what my random groupings table looks like in google slides. You can click the ‘update’ button at the top and the table will pull in any new kids that weren’t added before

If you want to try this out without doing the spreadsheet wrangling, I made a version that should be pretty easy to plug your classes into. All you basically need to do is:

Make your own sign-in sheet with 3 questions: Name, Period, and “Sign-In” or “Sign-Out”. It should look like this one: Randomizer Sign-In Sheet.

When you’ve made your sheet, click on the responses tab and click on the green square that allows you to view a spreadsheet. Make a new spreadsheet and call it whatever your heart desires.

Go to the Randomizer Spreadsheet (Here you can see the results of the sign-in sheet, as they come in from the form above, and you can see the results come in.

Go to the “Randomizer” tab of the spreadsheet above, and click on little menu on the right, then select the option “Copy to” and choose the sheet that you made in step 2.

It should almost be working, There is this one cell on the randomizer that is highlighted in orange that will have an error message. Click inside it, and confirm that it says “=arrayformula(‘Form Responses 1’!A:E)”. [Note: you shouldn’t have to alter anything, you should just have to double click and then press enter.]

So that’s my randomizer, let me know if you think it is useful. I can go more in depth about how it works but I want to say a little bit about why I think the class was better.

Today’s Firsts

Today’s class was a highlighted by a few small firsts. It was the first time that I tried to do a mid-work-time consolidate. This was an idea that I talked to someone about at NCTM Seattle and it was a move that would make a lot of sense. I wanted the kids to work on two sets of visual patterns one linear, and one quadratic, so I wanted to stop after the linear one and make sure everyone felt confident thinking about how we go about describing linear patterns before moving on. Once students got through with the linear set I could consolidate what we’ve all done as a class before moving on to the quadratic set of patterns. I was just about to do this mid lesson consolidation when I decided to roll out another first.

Almost all of the groups were at a linear equation for the first set of visual patterns except for one. This pairing was a girl who had only been in the class once before and another kid with better attendance whose work usually gets presented first and is kind of shy. Both students could use the confidence boost of figuring it out. They explained the equation in words, but somehow got stuck when it came time to write it on the dry erase contact paper that was attached to the storage closet in the back of class. While they were going back and forth about what to say I just sort of drifted away. My attention turned towards the front of the class where the two other groups were sitting idly with their linear equations locked and loaded. They would need to do something while we waited for the big consolidation, so I asked them to do a different problem as they waited, which was a first. For one group, a visual pattern that I had on the board got them immediately engaged. The other group was asked to look around the room at a problem they hadn’t done but others had. (In retrospect, I should have just given that second group the visual pattern as well because I think that group wasn’t as engaged in the consolidation later). In a few minutes we were able to do the halfway consolidation, with all groups feeling confident that they can handle any visual pattern I can throw at them.

All the groups had their confidence tested when they were faced with a non-linear visual pattern, and they were all able to use a recursive strategy and explicit strategy to find further patterns. It was actually pretty impressive seeing the group from the back of class with the most intuitive strategy to figure out what the equation was.

It was a pretty good day, I am not sure how I am going to get the kids who weren’t here (about 1/3 of the class) up to speed on what they missed. Any ideas?

Today I am about to get started on my Thinking Classroom experiment. I’m probably more nervous than I should be, so writing this will help. This post is to both organize my thoughts, and serve as a nice opening to a series of posts that I’ll write as this experiment unfolds. Today I am going to talk about what I’m going to try, but first I’ll recap how exactly this experiment came to be in the first place.

How this came to be

I was at the NCTM Regional in Kansas City, heading to an early morning shift at the #MTBOS booth, when the security guard informed me that the vendor area was closed. Naturally, I checked twitter, and saw a few tweets coming from a Peter Liljedahl session, so I headed over there to catch a little bit of the end. I proceeded to have my mind blown. Turns out the Thinking Classroom had dozens of great ideas behind it, and not just by the VNPS stuff:

@pgliljedahl Problem solving is what you do when you don’t know what to do. If you know what to do it’s exercising. A good problem is a problem where there is thinking left to do. #NCTMRegionals

@pgliljedahl When classes are too organized kids don’t really engage in thinking. Kids placed in a box keep their thinking in a box.What's the least amount of chaos you can add?. Defront the room. Have no discernable front and face kids in all sorts of different #NCTMRegionals

Having a classroom built around thinking was my plan for years! 3 years ago, I stopped calling my classes algebra and started calling them Mathematical Thinking, to signal that this is going to be a different experience. Liljedahl’s research laid out a 10 point plan for making the class into the experience that I hoped to create, with research and charts to back it all up. The biggest headline of the 10 point plan was the Vertical Non-Permanent Surfaces, which I had piloted last year. The session gave me some ideas about notes, assessment, and how the teacher provides more problems for the students as the class progresses.

After the talk, I headed back to the booth and talked with Joel Bezaire who had also done some Thinking Classroom stuff in his school. He made it seem really realistic. He told me about Dry Erase Contact Paper, the kinds of problems he uses, the spreadsheet that randomizes kids, and some of the blog posts he used. He also helped me think of ways to make it work at my school, which is not traditional and I don’t have as much time with my kids who all have really different abilities. In another stroke of luck, Peter Liljedahl was doing a session around the corner at the infinity bar after I finished talking to Joel. He was super nice and answered my questions until well over his allotted time. I also was able to download a lot DylanKane’sBlogPosts about the thinking classroom before my plane home took to read on the flight home. The fact that all these stars aligned made it clear that the universe wanted me to try the thinking classroom this cycle.

Fast forward to this morning. Things seem pretty much set. First off I have students! 11 students signed up for my class for this cycle, and a few more will trickle in which is good. This means getting kids into groups won’t be too hard, and I can save some of the whiteboard paper I would have used for a class of 30. As each kid signed up I showed them this video from Alex Overwijk, and explained some big ideas. “We’re going to do group work, and we’re not doing a whole bunch of worksheets. Instead, we’re going to maximize how much time you spend in class thinking…” Once class actually starts, I’ll need to reiterate the main ethos of what the class is, while also getting them immediately working. In the past I usually started class with a speech about me, my syllabus and how great our time together will be, but this is always boring and dry. Instead I’m going to explain a little bit about what we are doing, use the randomizer, and then get into some visual patterns and some function notation.

_______________________________

Update: I taught the first class and it was pretty interesting. The class was small in number with 4 kids of 11 kids (there was really bad weather last night, so it’s possible that people couldn’t make it in). The small class size could have been a good thing since it lowered the chances for a wide scale revolt. I made this randomizer that is basically the one Joel Bezaire described, with some modifications for my small class size, unpredictable attendance. The scary thing that comes along with small class size is the lack of different kinds of thinking. What if the small groups only come up with a couple of answers? Today the class all went through the visual patterns and came up with a few different ways to solve it. In the future, it will be hard to ensure that all of the different kinds of thinking that need to be elicited will actually show up. Maybe I’ll have to write up imaginary group work and post it somewhere else in the room as a “shadow group.”

The math wasn’t that substantial today, but we did plow through it. All the kids say they liked it and thought it was a fun. I am not clear on how we will introduce precise mathematical vocabulary and notation. Function notation will be the first thing we’ll see how it goes. Maybe I can just roll it out!

The first presentation of the day was a student presenting a math project about Misleading Graphs. This student clearly had no fear about this process. Earlier in the year he got on stage for the mental health panel and had also signed up to have 4 panels in one day. His confidence was as high as his substance as he was able to describe multiple types of misleading graphs and the news sources that keep making them. Even on the best presentations we have to keep asking questions that push the student. It is pretty rare when a student demonstrates total mastery over the math, the context, and the strategies the used. In this case, he didn’t really understand all the features he used on google sheets, and one graph that he made stepped over the line of being ‘misleading’ to just being incorrect. Presentations are great places to talk about wrong answers because you can really walk through the student about why it would be wrong, and correct any misconceptions on the spot. Sometimes even the teachers have misconceptions. That’s a great thing about presentations is that there is space to really root out any misconceptions.

Story 2: a kid comes in and says “my teacher is in the hospital, so they sent me to you to approve my independent project.” Independent projects have become a thing of the past thanks to me and the rest of the team. We’ve asked that projects that to be presented to only come class projects to avoid getting things that aren’t on a high school level. However, someone gave him a green light but couldn’t finally approve the work that the student did, so I had to step in and help him finish. The paper was titled “Old Testatement.” I was worried.

His paper was actually super interesting! He asked two questions. Could Adam and Eve have populated the Earth in the 6000 years since being cast out of the garden of Eden, and could the the earth have been covered by flood of Noah’s ark (which we learned was originally told in the Epic of Gilgamesh) have actually covered the Earth? It was brilliant! He made an exponential model to describe the growth of human population from Adam and Eve’s 44 kids, and used the volume formula to find out that the earth would have required 3 times the amount currently in the oceans to be as high as it was described in the book.

The ingenuity and the curiosity on display wasn’t the best part. He actually became a different math learner during his presentation. He was vocal about how much he hated math class, and this disdain was what led his teacher to go along with this independent project idea. He presented with three other kids, and offered to go first because he felt his project was the “least worthy.” But when he finished the kids sitting next to him said he did such a good job that they didn’t know how to follow it. We also commented on how well he answered questions and explored his original problem. He left the room with his back straight and his head held high.

It was a great example of independent thinking and what is possible when kids are pursuing their own questions. Now the policy around independent projects seems like it should be reconsidered. Or, we should have more opportunities for kids to do modelling tasks where they pursue questions as opposed to doing it just because. Having a ‘mythbusters’ class where the kids try to model some historical story or other event could be really interesting. Kids could also try and compete with each other and come up with the best model possible.

After a morning flash of insight, I spent way too much time on this Linear Regression Desmos Activity. It seemed like too cool of an idea to not do, although I’m sure it could be better. be For 4 weeks I’ve followed the IM 8th grade unit on data associations with my Algebra class, but I didn’t really have a cool way to talk about what linear regression is, or have a way to teach the kids how to use the regression features in Desmos. In retrospect, I could have sailed into the #MTBoS and found what other people are doing around regression, but I sort of burned my boats when I started making this thing. I trudged on in making this thing until 8 minutes before class, when I realized I needed make copies, and get upstairs. In all the work on the activity and the copies I didn’t get a chance to get the laptop key. We couldn’t use computers!

So I was up in the front of class, trying to keep my kids engaged while Jayla went to find the teacher who last had the laptop key (he was in the bathroom). “Alright guys, let’s review what we’ve been doing the last few days.” Doing a little mini-lesson at the board seemed like a good way to kill time. “How many people know what kind association this might be?” I said to the class while gesturing towards a hastily drawn scatterplot. Students looked back at me with silence and agony. It was clear they were not engaged, maybe because they knew the computers were coming. Their body language screamed that they were not invested in doing any part of this whole lecture thing. Then I thought to myself, “Teaching like this SUCKS.”

Over the past cycle I have been working on teaching with IM. Those materials have a lot more interaction, and realy prioritize the student voice. Kids were getting used to debating about which terms should be used, and agreeing on what is the right answer. There was a smooth flow to those classes while this little mini-lesson felt spreading the last of the natural peanut butter jar. The previous cycle I worked with a co-teacher who really pushed me to have more interactive lessons, with videos for the lectures, so I really haven’t done any kind of lecturing in a while. It really blows.

It set an awful tone for the Desmos Activity, which required a little bit of me in the driver seat since the activity was unclear in some parts. After the Desmos I had the last few lessons from the IM unit. The kids did a card sort, and used the card sort to learn about frequency tables and made some stacked bar charts. Everything felt kind of normal again.

Well kinda… I still need to fix that Desmos Activity, let me know if you have any feedback!

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Thanks everyone for coming! Here are the slides and a link to the google doc. Below is the google doc full of your ideas that we only temporarily destoryed: #NCTM Regionals Social Justice Ideas for Math Class